A soot-blackened fireplace that is believed to feature in one of Samuel Taylor Coleridge's most famous poems has been uncovered during a huge restoration project.

The Romantic poet wrote Frost at Midnight, which includes the description of a "thin blue flame" on "my low-burnt fire", while living at his cottage at Nether Stowey in Somerset.

As part of restoration work, the parlour fireplace, which had been bricked up, was exposed and refurbished, allowing visitors to get a feel for the spot where Coleridge may well have written one of his best-loved works.

Another intriguing feature is a representation in the garden of the lime tree bower in which Coleridge wrote This Lime-Tree Bower my Prison when he was unable to join William and Dorothy Wordsworth on a walk because his foot had been scalded with boiling milk.

The National Trust, which owns the cottage, and the Friends of Coleridge have worked together to restore the property, where the poet also wrote Kubla Khan and The Rime of the Ancient Mariner.

Simon Jenkins, the National Trust chairman, planted another lime tree in the garden of Coleridge Cottage on Friday to mark the end of the project.

The rooms – parlours, kitchen, bedrooms – and the garden are designed to give an impression of how the cottage would have looked in Coleridge's day and also tell some of the stories of his life.

His poetry (and addiction to opium) are well known but the custodians of his cottage have tried to highlight his talents as a journalist, diplomat, playwright, translator, philosopher, metaphysician and brilliant orator and communicator.

Matthew Oates, a naturalist at the National Trust and a Coleridge enthusiast, said: "If Coleridge were alive today he would be a major media celebrity, offering his radical views on topics of interest from science to the arts. He remains one of the greatest minds this country has produced.

"His deep love of the countryside – and its huge importance on his writing – comes through strongly in the new presentation. The cottage feels as if the Coleridge family have just stepped out for a moment, a place where visitors can immerse themselves in the period and learn much more about one of the great men of the past."